{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Demo of rolling shutter compensation\n",
    "This notebook provides an example of how rolling shutter and sensor velocity arguments are applied in the rasterization.\n",
    "While this demonstration focuses on camera rasterization, the same principles also apply to lidar rasterization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import torch\n",
    "from gsplat.rendering import rasterization\n",
    "\n",
    "assert torch.cuda.is_available(), \"This demo requires a GPU with CUDA support.\"\n",
    "device = torch.device(\"cuda\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Setting up the test data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Gaussian parameters, defined in camera coordinate system for simplicity\n",
    "N = 20\n",
    "means = torch.zeros(N, 3, device=device)\n",
    "means[:, 2] = 10\n",
    "means[:, 1] = torch.linspace(-5, 5, N, device=device)\n",
    "quats = torch.tensor([[1., 0., 0., 0.]] * N, device=device)\n",
    "scales = torch.ones(N, 3, device=device) * 0.1\n",
    "opacities = torch.ones(N, device=device)\n",
    "velocities = torch.zeros(N, 3, device=device)\n",
    "colors = torch.zeros(N, 3, device=device)\n",
    "colors[:, 1] = torch.linspace(0, 1, N, device=device)\n",
    "colors[:, 2] = torch.linspace(1, 0, N, device=device)\n",
    "\n",
    "# Camera parameters\n",
    "viewmats = torch.tensor([\n",
    "    [1., 0., 0., 0.],\n",
    "    [0., 1., 0., 0.],\n",
    "    [0., 0., 1., 0.],\n",
    "    [0., 0., 0., 1.]\n",
    "], device=device).view(1, 4, 4)\n",
    "H, W = 500, 500\n",
    "focal = 500\n",
    "K = torch.tensor([[focal, 0., W / 2],\n",
    "                  [0., focal, H / 2],\n",
    "                  [0., 0., 1.]], device=device).view(1, 3, 3)\n",
    "\n",
    "# Plot our test data\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "ax.scatter(means[:, 2].cpu(), means[:, 0].cpu(), -means[:, 1].cpu(), c=colors.cpu(), label=\"3D Gaussians\")\n",
    "ax.scatter(0, 0, 0, c='r', label='Camera')\n",
    "ax.quiver(0, 0, 0, 0, 1, 0, color='r') # camera x-axis\n",
    "ax.quiver(0, 0, 0, 0, 0, -1, color='g') # camera y-axis\n",
    "ax.quiver(0, 0, 0, 1, 0, 0, color='b') # camera z-axis\n",
    "ax.axis(\"equal\")\n",
    "ax.invert_yaxis()\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Without rolling shutter\n",
    "The parameters related to rolling shutter are `linear_velocity`, `angular_velocity`, `rolling_shutter_time` and `velocities`:\n",
    "- Linear and angular velocity: Represent the movement of the sensor (in this case, the camera) within its own coordinate system.\n",
    "- Rolling shutter time: Indicates the duration required for the sensor to complete a full scan.\n",
    "- Velocities: The 3D velocities of the Gaussians, expressed in their own coordinate system.\n",
    "\n",
    "If the sensor's velocity is set to zero, it remains stationary, and no rolling shutter compensation is applied during rasterization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "linear_velocity = torch.zeros(1, 3, device=device)\n",
    "angular_velocity = torch.zeros(1, 3, device=device)\n",
    "rolling_shutter_time = torch.zeros(1, device=device)\n",
    "\n",
    "colors_out, _, _ = rasterization(\n",
    "    means=means,\n",
    "    quats=quats,\n",
    "    scales=scales,\n",
    "    opacities=opacities,\n",
    "    colors=colors,\n",
    "    velocities=velocities,\n",
    "    viewmats=viewmats,\n",
    "    Ks=K,\n",
    "    width=W,\n",
    "    height=H,\n",
    "    linear_velocity=linear_velocity,\n",
    "    angular_velocity=angular_velocity,\n",
    "    rolling_shutter_time=rolling_shutter_time,\n",
    "    sh_degree=None,\n",
    "    render_mode=\"RGB\",\n",
    "    packed=False,\n",
    ")\n",
    "\n",
    "# Plot the image\n",
    "plt.figure()\n",
    "plt.imshow(colors_out.squeeze(0).cpu())\n",
    "plt.title(\"With stationary camera\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### With rolling shutter compensation\n",
    "When a sensor moves during capture, it introduces the rolling shutter effect (assuming that the data is not captured instantenous). This effect can be simulated during rasterization by applying appropriate sensor velocities and rolling shutter parameters.\n",
    "\n",
    "For instance, consider a camera traveling along the x-axis in the camera's coordinate system:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "linear_velocity = torch.tensor([[1., 0., 0.]], device=device) * 30\n",
    "angular_velocity = torch.zeros(1, 3, device=device)\n",
    "rolling_shutter_time = torch.ones(1, device=device) * 0.05\n",
    "\n",
    "colors_out, _, _ = rasterization(\n",
    "    means=means,\n",
    "    quats=quats,\n",
    "    scales=scales,\n",
    "    opacities=opacities,\n",
    "    colors=colors,\n",
    "    velocities=velocities,\n",
    "    viewmats=viewmats,\n",
    "    Ks=K,\n",
    "    width=W,\n",
    "    height=H,\n",
    "    linear_velocity=linear_velocity,\n",
    "    angular_velocity=angular_velocity,\n",
    "    rolling_shutter_time=rolling_shutter_time,\n",
    "    sh_degree=None,\n",
    "    render_mode=\"RGB\",\n",
    "    packed=False,\n",
    ")\n",
    "\n",
    "# Plot the image\n",
    "plt.figure()\n",
    "plt.imshow(colors_out.squeeze(0).cpu())\n",
    "plt.title(\"With moving camera\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The rolling shutter time can be adjusted to simulate a slower camera capture:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "linear_velocity = torch.tensor([[1., 0., 0.]], device=device) * 30\n",
    "angular_velocity = torch.zeros(1, 3, device=device)\n",
    "rolling_shutter_time = torch.ones(1, device=device) * 0.5\n",
    "\n",
    "colors_out, _, _ = rasterization(\n",
    "    means=means,\n",
    "    quats=quats,\n",
    "    scales=scales,\n",
    "    opacities=opacities,\n",
    "    colors=colors,\n",
    "    velocities=velocities,\n",
    "    viewmats=viewmats,\n",
    "    Ks=K,\n",
    "    width=W,\n",
    "    height=H,\n",
    "    linear_velocity=linear_velocity,\n",
    "    angular_velocity=angular_velocity,\n",
    "    rolling_shutter_time=rolling_shutter_time,\n",
    "    sh_degree=None,\n",
    "    render_mode=\"RGB\",\n",
    "    packed=False,\n",
    ")\n",
    "\n",
    "# Plot the image\n",
    "plt.figure()\n",
    "plt.imshow(colors_out.squeeze(0).cpu())\n",
    "plt.title(\"With moving camera and longer rolling shutter time\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Angular velocities can also contribute to the rolling shutter effect:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "linear_velocity = torch.zeros(1, 3, device=device)\n",
    "angular_velocity = torch.tensor([[0., 1., 0.]], device=device) * 5.0\n",
    "rolling_shutter_time = torch.ones(1, device=device) * 0.05\n",
    "\n",
    "colors_out, _, _ = rasterization(\n",
    "    means=means,\n",
    "    quats=quats,\n",
    "    scales=scales,\n",
    "    opacities=opacities,\n",
    "    colors=colors,\n",
    "    velocities=velocities,\n",
    "    viewmats=viewmats,\n",
    "    Ks=K,\n",
    "    width=W,\n",
    "    height=H,\n",
    "    linear_velocity=linear_velocity,\n",
    "    angular_velocity=angular_velocity,\n",
    "    rolling_shutter_time=rolling_shutter_time,\n",
    "    sh_degree=None,\n",
    "    render_mode=\"RGB\",\n",
    "    packed=False,\n",
    ")\n",
    "\n",
    "# Plot the image\n",
    "plt.figure()\n",
    "plt.imshow(colors_out.squeeze(0).cpu())\n",
    "plt.title(\"With rotating camera\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The rolling shutter effect can also appear in stationary sensors when observing fast-moving objects. This can be simulated using the `velocities` argument:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "linear_velocity = torch.zeros(1, 3, device=device)\n",
    "angular_velocity = torch.tensor([[0., 1., 0.]], device=device)\n",
    "rolling_shutter_time = torch.ones(1, device=device) * 0.05\n",
    "velocities[:, 0] = 30.0\n",
    "\n",
    "colors_out, _, _ = rasterization(\n",
    "    means=means,\n",
    "    quats=quats,\n",
    "    scales=scales,\n",
    "    opacities=opacities,\n",
    "    colors=colors,\n",
    "    velocities=velocities,\n",
    "    viewmats=viewmats,\n",
    "    Ks=K,\n",
    "    width=W,\n",
    "    height=H,\n",
    "    linear_velocity=linear_velocity,\n",
    "    angular_velocity=angular_velocity,\n",
    "    rolling_shutter_time=rolling_shutter_time,\n",
    "    sh_degree=None,\n",
    "    render_mode=\"RGB\",\n",
    "    packed=False,\n",
    ")\n",
    "\n",
    "# Plot the image\n",
    "plt.figure()\n",
    "plt.imshow(colors_out.squeeze(0).cpu())\n",
    "plt.title(\"With moving Gaussians\")\n",
    "plt.show()"
   ]
  }
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